Local electromagnetic duality and gauge invariance

Abstract

Bunster and Henneaux and, separately, Deser have very recently considered the possibility of gauging the usual electromagnetic duality of Maxwell equations. By using off-shell manipulations in the context of the principle of least action, they conclude that this is not possible, at least with the conventional compensating gauge field scheme. Such a conclusion, however, contradicts an old result of Malik and Pradhan, who showed that it is indeed possible to introduce an extra Abelian gauge field directly in the vacuum Maxwell equations in order to render them covariant under local duality transformations. Since it is well known that the equations of motion can, in general, admit more symmetries than the associate Lagrangian, this would not be a paradoxal result, in principle. Here, we revisit these works and identify the source of the different conclusions. We show that the Malik–Pradhan procedure does not preserve the original Maxwell gauge invariance, while Bunster, Henneaux and Deser sought for generalizations which are, by construction, invariant under the Maxwell gauge transformation. Further, we show that the Malik–Pradhan construction cannot be adapted or extended in order to preserve the Maxwell gauge invariance, reinforcing the conclusion that it is not possible to gauge the electromagnetic duality.